TLmoms {lmomco} | R Documentation

## The Sample Trimmed L-moments and L-moment Ratios

### Description

Compute the sample trimmed L-moments (TL-moments) for a vector. The level of symmetrical trimming is specified. A TL-moment is

hat{λ}^{(t_1,t_2)}_r = frac{1}{r}sum^{n-t_2}_{i=t_1+1} <=ft[ frac{sumlimits^{r-1}_{k=0}{ (-1)^k {r-1 choose k} {i-1 choose r+t_1-1-k} {n-i choose t_2+k} }}{{n choose r+t_1+t_2}} right] x_{i:n} mbox{,}

where t_a represents the trimming level of the t_2-largest or t_1-smallest values, r represents the order of the L-moments, n represents the sample size, and x_{i:n} represents the ith sample order statistic (x_{1:n} <= x_{2:n} <= ... <= x_{n:n}). This function loops across the above equation for each `nmom` set in the argument list.

### Usage

    TLmoms(x,nmom,trim=NULL,leftrim=NULL,rightrim=NULL)

### Arguments

`x` | A vector of data values.
`nmom` | The number of moments to compute. Default is 5.
`trim` | Level of symmetrical trimming to use in the computations, which will equal `NULL` if asymmetrical trimming was used. Although `NULL` in the argument list, the default is 0—the usual L-moment is returned.
`leftrim` | Level of trimming of the left-tail of the sample.
`rightrim` | Level of trimming of the right-tail of the sample.

### Value

An R `list` is returned.

`lambdas` | Vector of the TL-moments. First element is hat{λ}^{(t_1,t_2)}_1, second element is hat{λ}^{(t_1,t_2)}_2, and so on.
`ratios` | Vector of the L-moment ratios. Second element is hat{tau}^{(t_1,t_2)}, third element is hat{tau}^{(t_1,t_2)}_3 and so on.
`trim` | Level of symmetrical trimming used in the computation, which will equal `NULL` if asymmetrical trimming was used.
`leftrim` | Level of left-tail trimming used in the computation.
`rightrim` | Level of right-tail trimming used in the computation.
`source` | An attribute identifying the computational source of the L-moments: “TLmoms”.

### Note

It is important to note that the “L-moment object” returned by `TLmoms` is different in structure to that returned by `lmom.ub`, `pwm2lmom`, and similar as the TL-moments should not be confused with the ordinary L-moments. Implementation in the package might change.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational statistics and data analysis, vol. 43, pp. 299-314.

### See Also

`TLmom`, `lmoms`, and `lmorph`

### Examples

    X1 <- rcauchy(30)
    TL <- TLmoms(X1,nmom=6,trim=1)

[Package lmomco version 0.92 Index]